A large number of relevant parameters for such a system can be estimated using scaling laws of LWFAs [1]} and FELs [2]}. These parameters are listed in Table REF . The parameters are estimated self-consistently balancing multiple constraints at different stages of the machine.
Order-of-magnitude estimates based on parameters summarized in Table REF  show that it is possible to design an FEL at hard x-ray wavelengths, which is based on the laser accelerator technology. External injection of electrons into the plasma accelerator results in a beam of a high enough quality to achieve lasing.
